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Proof step 3 from proof div2-neg-odd (previous step)

j < 0 ⊦ (j * 2 - 1) / 2 = ~((~ j * 2 + 1) / 2), (j * 2 - 1) / 2 = j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ j ≠ 0 → ~ i / j = ~(i / j)

Rule argument

spec: int-div inst: name: Div-left seq: ⊦ j ≠ 0 → ~ i / j = ~(i / j) subst: [j, i] → [2, ~ j * 2 + 1] flags: rewrite, current

Additional information

Used simplifier rules: minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%minus-sub: ⊦ ~(i - j) = j - i; from specification int-abs Used terms: 2, ~ j * 2 + 1